Abstract
It is a folklore result that testing whether a given system of equations with two variables per inequality (a 2VPI system) of the form x i − x j = c ij is solvable, can be done efficiently not only by Gaussian elimination but also by shortest-path computation on an associated constraint graph. However, when the system is infeasible and one wishes to delete a minimum weight set of inequalities to obtain feasibility (MinFs2 =), this task becomes NP-complete.
Our main result is a 2-approximation for the problem MinFs2 = for the case when the constraint graph is planar using a primal-dual approach. We also give an α-approximation for the related maximization problem MaxFs2 = where the goal is to maximize the weight of feasible inequalities. Here, α denotes the arboricity of the constraint graph. Our results extend to obtain constant factor approximations for the case when the domains of the variables are further restricted.
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Leithäuser, N., Krumke, S.O., Merkert, M. (2012). Approximating Infeasible 2VPI-Systems. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_24
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DOI: https://doi.org/10.1007/978-3-642-34611-8_24
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